ESG Considerations for Securitized Fixed Income Notes
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Portfolio Optimization with Drawdown Constraints
Implemented in Portfolio Safeguard by AOrDa.com PORTFOLIO OPTIMIZATION WITH DRAWDOWN CONSTRAINTS Alexei Chekhlov1, Stanislav Uryasev2, Michael Zabarankin2 Risk Management and Financial Engineering Lab Center for Applied Optimization Department of Industrial and Systems Engineering University of Florida, Gainesville, FL 32611 Date: January 13, 2003 Correspondence should be addressed to: Stanislav Uryasev Abstract We propose a new one-parameter family of risk functions defined on portfolio return sample -paths, which is called conditional drawdown-at-risk (CDaR). These risk functions depend on the portfolio drawdown (underwater) curve considered in active portfolio management. For some value of the tolerance parameter a , the CDaR is defined as the mean of the worst (1-a) *100% drawdowns. The CDaR risk function contains the maximal drawdown and average drawdown as its limiting cases. For a particular example, we find optimal portfolios with constraints on the maximal drawdown, average drawdown and several intermediate cases between these two. The CDaR family of risk functions originates from the conditional value-at-risk (CVaR) measure. Some recommendations on how to select the optimal risk measure for getting practically stable portfolios are provided. We solved a real life portfolio allocation problem using the proposed risk functions. 1. Introduction Optimal portfolio allocation is a longstanding issue in both practical portfolio management and academic research on portfolio theory. Various methods have been proposed and studied (for a review, see, for example, Grinold and Kahn, 1999). All of them, as a starting point, assume some measure of portfolio risk. From a standpoint of a fund manager, who trades clients' or bank’s proprietary capital, and for whom the clients' accounts are the only source of income coming in the form of management and incentive fees, losing these accounts is equivalent to the death of his business. -
Initial Public Offerings
November 2017 Initial Public Offerings An Issuer’s Guide (US Edition) Contents INTRODUCTION 1 What Are the Potential Benefits of Conducting an IPO? 1 What Are the Potential Costs and Other Potential Downsides of Conducting an IPO? 1 Is Your Company Ready for an IPO? 2 GETTING READY 3 Are Changes Needed in the Company’s Capital Structure or Relationships with Its Key Stockholders or Other Related Parties? 3 What Is the Right Corporate Governance Structure for the Company Post-IPO? 5 Are the Company’s Existing Financial Statements Suitable? 6 Are the Company’s Pre-IPO Equity Awards Problematic? 6 How Should Investor Relations Be Handled? 7 Which Securities Exchange to List On? 8 OFFER STRUCTURE 9 Offer Size 9 Primary vs. Secondary Shares 9 Allocation—Institutional vs. Retail 9 KEY DOCUMENTS 11 Registration Statement 11 Form 8-A – Exchange Act Registration Statement 19 Underwriting Agreement 20 Lock-Up Agreements 21 Legal Opinions and Negative Assurance Letters 22 Comfort Letters 22 Engagement Letter with the Underwriters 23 KEY PARTIES 24 Issuer 24 Selling Stockholders 24 Management of the Issuer 24 Auditors 24 Underwriters 24 Legal Advisers 25 Other Parties 25 i Initial Public Offerings THE IPO PROCESS 26 Organizational or “Kick-Off” Meeting 26 The Due Diligence Review 26 Drafting Responsibility and Drafting Sessions 27 Filing with the SEC, FINRA, a Securities Exchange and the State Securities Commissions 27 SEC Review 29 Book-Building and Roadshow 30 Price Determination 30 Allocation and Settlement or Closing 31 Publicity Considerations -
Portfolio Optimization with Drawdown Constraints
PORTFOLIO OPTIMIZATION WITH DRAWDOWN CONSTRAINTS Alexei Chekhlov1, Stanislav Uryasev2, Michael Zabarankin2 Risk Management and Financial Engineering Lab Center for Applied Optimization Department of Industrial and Systems Engineering University of Florida, Gainesville, FL 32611 Date: January 13, 2003 Correspondence should be addressed to: Stanislav Uryasev Abstract We propose a new one-parameter family of risk functions defined on portfolio return sample -paths, which is called conditional drawdown-at-risk (CDaR). These risk functions depend on the portfolio drawdown (underwater) curve considered in active portfolio management. For some value of the tolerance parameter a , the CDaR is defined as the mean of the worst (1-a) *100% drawdowns. The CDaR risk function contains the maximal drawdown and average drawdown as its limiting cases. For a particular example, we find optimal portfolios with constraints on the maximal drawdown, average drawdown and several intermediate cases between these two. The CDaR family of risk functions originates from the conditional value-at-risk (CVaR) measure. Some recommendations on how to select the optimal risk measure for getting practically stable portfolios are provided. We solved a real life portfolio allocation problem using the proposed risk functions. 1. Introduction Optimal portfolio allocation is a longstanding issue in both practical portfolio management and academic research on portfolio theory. Various methods have been proposed and studied (for a review, see, for example, Grinold and Kahn, 1999). All of them, as a starting point, assume some measure of portfolio risk. From a standpoint of a fund manager, who trades clients' or bank’s proprietary capital, and for whom the clients' accounts are the only source of income coming in the form of management and incentive fees, losing these accounts is equivalent to the death of his business. -
T013 Asset Allocation Minimizing Short-Term Drawdown Risk And
Asset Allocation: Minimizing Short-Term Drawdown Risk and Long-Term Shortfall Risk An institution’s policy asset allocation is designed to provide the optimal balance between minimizing the endowment portfolio’s short-term drawdown risk and minimizing its long-term shortfall risk. Asset Allocation: Minimizing Short-Term Drawdown Risk and Long-Term Shortfall Risk In this paper, we propose an asset allocation framework for long-term institutional investors, such as endowments, that are seeking to satisfy annual spending needs while also maintaining and growing intergenerational equity. Our analysis focuses on how asset allocation contributes to two key risks faced by endowments: short-term drawdown risk and long-term shortfall risk. Before approving a long-term asset allocation, it is important for an endowment’s board of trustees and/or investment committee to consider the institution’s ability and willingness to bear two risks: short-term drawdown risk and long-term shortfall risk. We consider various asset allocations along a spectrum from a bond-heavy portfolio (typically considered “conservative”) to an equity-heavy portfolio (typically considered “risky”) and conclude that a typical policy portfolio of 60% equities, 30% bonds, and 10% real assets represents a good balance between these short-term and long-term risks. We also evaluate the impact of alpha generation and the choice of spending policy on an endowment’s expected risk and return characteristics. We demonstrate that adding alpha through manager selection, tactical asset allocation, and the illiquidity premium significantly reduces long-term shortfall risk while keeping short-term drawdown risk at a desired level. We also show that even a small change in an endowment’s spending rate can significantly impact the risk profile of the portfolio. -
A Nonlinear Optimisation Model for Constructing Minimal Drawdown Portfolios
A nonlinear optimisation model for constructing minimal drawdown portfolios C.A. Valle1 and J.E. Beasley2 1Departamento de Ci^enciada Computa¸c~ao, Universidade Federal de Minas Gerais, Belo Horizonte, MG 31270-010, Brazil [email protected] 2Mathematical Sciences, Brunel University, Uxbridge UB8 3PH, UK [email protected] August 2019 Abstract In this paper we consider the problem of minimising drawdown in a portfolio of financial assets. Here drawdown represents the relative opportunity cost of the single best missed trading opportunity over a specified time period. We formulate the problem (minimising average drawdown, maximum drawdown, or a weighted combination of the two) as a non- linear program and show how it can be partially linearised by replacing one of the nonlinear constraints by equivalent linear constraints. Computational results are presented (generated using the nonlinear solver SCIP) for three test instances drawn from the EURO STOXX 50, the FTSE 100 and the S&P 500 with daily price data over the period 2010-2016. We present results for long-only drawdown portfolios as well as results for portfolios with both long and short positions. These indicate that (on average) our minimal drawdown portfolios dominate the market indices in terms of return, Sharpe ratio, maximum drawdown and average drawdown over the (approximately 1800 trading day) out-of-sample period. Keywords: Index out-performance; Nonlinear optimisation; Portfolio construction; Portfo- lio drawdown; Portfolio optimisation 1 Introduction Given a portfolio of financial assets then, as time passes, the price of each asset changes and so by extension the value of the portfolio changes. -
Maximum Drawdown Is Generally Greater Than in IID Normal Case
THE HIGH COST OF SIMPLIFIED MATH: Overcoming the “IID Normal” Assumption in Performance Evaluation Marcos López de Prado Hess Energy Trading Company Lawrence Berkeley National Laboratory Electronic copy available at: http://ssrn.com/abstract=2254668 Key Points • Investment management firms routinely hire and fire employees based on the performance of their portfolios. • Such performance is evaluated through popular metrics that assume IID Normal returns, like Sharpe ratio, Sortino ratio, Treynor ratio, Information ratio, etc. • Investment returns are far from IID Normal. • If we accept first-order serial correlation: – Maximum Drawdown is generally greater than in IID Normal case. – Time Under Water is generally longer than in IID Normal case. – However, Penance is typically shorter than 3x (IID Normal case). • Conclusion: Firms evaluating performance through Sharpe ratio are firing larger numbers of skillful managers than originally targeted, at a substantial cost to investors. 2 Electronic copy available at: http://ssrn.com/abstract=2254668 SECTION I The Need for Performance Evaluation Electronic copy available at: http://ssrn.com/abstract=2254668 Why Performance Evaluation? • Hedge funds operate as banks lending money to Portfolio Managers (PMs): – This “bank” charges ~80% − 90% on the PM’s return (not the capital allocated). – Thus, it requires each PM to outperform the risk free rate with a sufficient confidence level: Sharpe ratio. – This “bank” pulls out the line of credit to underperforming PMs. Allocation 1 … Investors’ funds Allocation N 4 How much is Performance Evaluation worth? • A successful hedge fund serves its investors by: – building and retaining a diversified portfolio of truly skillful PMs, taking co-dependencies into account, allocating capital efficiently. -
Timken.Com: Board of Directors General Policies and Procedures
2019 EXHIBIT A THE TIMKEN COMPANY BOARD OF DIRECTORS GENERAL POLICIES AND PROCEDURES The primary duty of the Board of Directors (the “Board”) is to promote the best interests of the Company through overseeing the management of the Company’s business and affairs. In doing so, the directors must consider the interests of the Company’s shareholders. These guidelines have been adopted to facilitate execution of this responsibility and will be reviewed annually by the Nominating and Corporate Governance Committee of the Board. Director Responsibilities In discharging their obligations, directors are entitled to rely on the honesty and integrity of the Company’s senior executives and its outside advisors and auditors. Board members are expected to review meeting materials in advance, to attend and participate in all Board meetings and meetings of Board committees on which they serve and to devote the time necessary to discharge their responsibilities appropriately. Directors are required to abide by the Company’s Standards of Business Ethics Policy. The Nominating and Corporate Governance Committee will oversee an annual self-evaluation of the Board to determine whether it and its committees are functioning effectively. Director Selection Selection of Nominees. The Nominating and Corporate Governance Committee is responsible for recommending candidates for Board membership to the Board. General criteria for nomination of director candidates include, but are not limited to, the highest standards of integrity and ethical behavior, the ability to provide wise and informed guidance to management, a willingness to pursue thoughtful, objective inquiry on important issues before the Company, and a range of experience and knowledge commensurate with the Company’s needs as well as the expectations of knowledgeable investors. -
Capital Adequacy Requirements (CAR)
Guideline Subject: Capital Adequacy Requirements (CAR) Chapter 3 – Credit Risk – Standardized Approach Effective Date: November 2017 / January 20181 The Capital Adequacy Requirements (CAR) for banks (including federal credit unions), bank holding companies, federally regulated trust companies, federally regulated loan companies and cooperative retail associations are set out in nine chapters, each of which has been issued as a separate document. This document, Chapter 3 – Credit Risk – Standardized Approach, should be read in conjunction with the other CAR chapters which include: Chapter 1 Overview Chapter 2 Definition of Capital Chapter 3 Credit Risk – Standardized Approach Chapter 4 Settlement and Counterparty Risk Chapter 5 Credit Risk Mitigation Chapter 6 Credit Risk- Internal Ratings Based Approach Chapter 7 Structured Credit Products Chapter 8 Operational Risk Chapter 9 Market Risk 1 For institutions with a fiscal year ending October 31 or December 31, respectively Banks/BHC/T&L/CRA Credit Risk-Standardized Approach November 2017 Chapter 3 - Page 1 Table of Contents 3.1. Risk Weight Categories ............................................................................................. 4 3.1.1. Claims on sovereigns ............................................................................... 4 3.1.2. Claims on unrated sovereigns ................................................................. 5 3.1.3. Claims on non-central government public sector entities (PSEs) ........... 5 3.1.4. Claims on multilateral development banks (MDBs) -
Multi-Period Portfolio Selection with Drawdown Control
Author's personal copy Annals of Operations Research (2019) 282:245–271 https://doi.org/10.1007/s10479-018-2947-3 S.I.: APPLICATION OF O. R. TO FINANCIAL MARKETS Multi-period portfolio selection with drawdown control Peter Nystrup1,2 · Stephen Boyd3 · Erik Lindström4 · Henrik Madsen1 Published online: 20 June 2018 © Springer Science+Business Media, LLC, part of Springer Nature 2018 Abstract In this article, model predictive control is used to dynamically optimize an investment port- folio and control drawdowns. The control is based on multi-period forecasts of the mean and covariance of financial returns from a multivariate hidden Markov model with time- varying parameters. There are computational advantages to using model predictive control when estimates of future returns are updated every time new observations become available, because the optimal control actions are reconsidered anyway. Transaction and holding costs are discussed as a means to address estimation error and regularize the optimization problem. The proposed approach to multi-period portfolio selection is tested out of sample over two decades based on available market indices chosen to mimic the major liquid asset classes typ- ically considered by institutional investors. By adjusting the risk aversion based on realized drawdown, it successfully controls drawdowns with little or no sacrifice of mean–variance efficiency. Using leverage it is possible to further increase the return without increasing the maximum drawdown. Keywords Risk management · Maximum drawdown · Dynamic asset allocation · Model predictive control · Regime switching · Forecasting This work was supported by Sampension and Innovation Fund Denmark under Grant No. 4135-00077B.. B Peter Nystrup [email protected] Stephen Boyd [email protected] Erik Lindström [email protected] Henrik Madsen [email protected] 1 Department of Applied Mathematics and Computer Science, Technical University of Denmark, Asmussens Allé, Building 303B, 2800 Kgs. -
Philips Lighting Prospectus.Pdf
(Philips Lighting N.V., a public company with limited liability (naamloze vennootschap) incorporated under the laws of the Netherlands, with its corporate seat in Eindhoven, the Netherlands) Initial Public Offering of 37,500,000 ordinary shares Koninklijke Philips N.V. (the “Selling Shareholder”) is offering 37,500,000 ordinary shares in the share capital of the Company (as defined below) with a nominal value of €0.01 each (the “Offer Shares”, which include, unless the context indicates otherwise, the Over-Allotment Shares (as defined below)). Assuming no exercise of the Over-Allotment Option (as defined below), the Offer Shares will constitute 25% of the issued and outstanding ordinary shares in the share capital of the Company with a nominal value of €0.01 each (the “Ordinary Shares”). Except where the context otherwise requires, references to the Ordinary Shares will be deemed to include the Offer Shares. Assuming the Over-Allotment Option is fully exercised, the Offer Shares will constitute 28.75% of the Ordinary Shares. See “The Offering”. The offering of the Offer Shares (the “Offering”) consists of (i) a public offering in the Netherlands to institutional and retail investors and (ii) a private placement to (a) investors outside the Netherlands and the United States of America (the “U.S.”or“United States”) subject to applicable exemptions from the prospectus requirements and (b) investors in the United States reasonably believed to be “qualified institutional buyers” (“QIBs”) as defined in Rule 144A under the U.S. Securities Act of 1933, as amended (the “U.S. Securities Act”) (“Rule 144A”). All offers and sales in the United States will be made only to persons reasonably believed to be QIBs in reliance on Rule 144A. -
What Do One Million Credit Line Observations Tell Us About Exposure at Default? a Study of Credit Line Usage by Spanish Firms
What Do One Million Credit Line Observations Tell Us about Exposure at Default? A Study of Credit Line Usage by Spanish Firms Gabriel Jiménez Banco de España [email protected] Jose A. Lopez Federal Reserve Bank of San Francisco [email protected] Jesús Saurina Banco de España [email protected] DRAFT…….Please do not cite without authors’ permission Draft date: June 16, 2006 ABSTRACT Bank credit lines are a major source of funding and liquidity for firms and a key source of credit risk for the underwriting banks. In fact, credit line usage is addressed directly in the current Basel II capital framework through the exposure at default (EAD) calculation, one of the three key components of regulatory capital calculations. Using a large database of Spanish credit lines across banks and years, we model the determinants of credit line usage by firms. We find that the risk profile of the borrowing firm, the risk profile of the lender, and the business cycle have a significant impact on credit line use. During recessions, credit line usage increases, particularly among the more fragile borrowers. More importantly, we provide robust evidence of more intensive use of credit lines by borrowers that later default on those lines. Our data set allows us to enter the policy debate on the EAD components of the Basel II capital requirements through the calculation of credit conversion factors (CCF) and loan equivalent exposures (LEQ). We find that EAD exhibits procyclical characteristics and is affected by credit line characteristics, such as commitment size, maturity, and collateral requirements. -
Implementing and Testing the Maximum Drawdown at Risk
Finance Research Letters 22 (2017) 95–100 Contents lists available at ScienceDirect Finance Research Letters journal homepage: www.elsevier.com/locate/frl Implementing and testing the Maximum Drawdown at Risk ∗ Beatriz Vaz de Melo Mendes a, , Rafael Coelho Lavrado b a COPPEAD/IM, Federal University at Rio de Janeiro, Brazil b IMPA, Instituto Nacional de Matemática Pura e Aplicada, Brazil a r t i c l e i n f o a b s t r a c t Article history: Financial managers are mainly concerned about long lasting accumulated large losses Received 22 October 2016 which may lead to massive money withdrawals. To assess this risk feeling we compute Revised 26 May 2017 the Maximum Drawdown, the largest price loss of an investment during some fixed time Accepted 3 June 2017 period. The Maximum Drawdown at Risk has become an important risk measure for com- Available online 9 June 2017 modity trading advisors, hedge funds managers, and regulators. In this study we propose JEL classification: an estimation methodology based on Monte Carlo simulations and empirically validate the C14 procedure using international stock indices. We find that this tool provides more accurate C15 market risk control and may be used to manage portfolio exposure, being useful to practi- C53 tioners and financial analysts. C58 ©2017 Elsevier Inc. All rights reserved. G32 Keywords: Risk management Maximum drawdown ARMA-GARCH Simulations 1. Introduction Financial managers are mainly concerned about large losses because they may destroy accumulated wealth leading to massive money withdrawals and risking the continuity of businesses. Financial crises such as the 2008 global one have shown how extensive these losses could be, with investment funds all over the world showing more than 50% losses and survivors taking several years to recover.